Alien Worlds

 Netflix just released a new documentary/sci-fi series in which they imagine what life is like on planets discovered outside our solar system. In creating these worlds, they imagine a planet Atlas just outside the Milky Way which is twice as large as Earth. They then try to conceptualize how animals might adapt on this new planet. Their imaginary predators, small bug like creatures, are able to absorb small, hydrogen emitting bacteria. As the bacteria release hydrogen gas as part of their metabolism, a small sac attached to the back of the bug fills with air and the bugs float to 1,000 ft (or about 305m) above the ground. They then release the gas, sending themselves into free fall and latch onto their pray: big bird-like creatures that fly slightly lower at just under 200m off the ground. 

After watching this show and discussing buoyancy in class, I began to wonder how much hydrogen gas would be needed to lift the bug off the ground in an environment with twice as much gravity as Earth. First I had to approximate the mass of the bug. In comparing these animals to earth-like creatures, researchers equated the bug to a rhinoceros beetle, or the largest beetle on Earth. The rhinoceros beetle has a mass of about 100grams; I decided to use this as the mass of the bug. In order to have an upwards acceleration, the buoyant force must exceed the weight of the bug and the weight of the air. This leads to the equation:

Fb-weight full air sac-weight bug>0

(p air)(V air displaced)(g)-(p hydrogen)(V sac)(g)-(m)(g)>0

On this imaginary planet, the average air density is assumed to be 6.5kg/m3 and the acceleration due to gravity is 20.49m/s2. Assuming that the density of hydrogen gas follows the same ratio as the average density of air (the air is 5.4x as dense on Atlas), the density of hydrogen gas will be around (0.082kg/m3)(5.4)=0.4428

If we plug these into our equation we get:

((Vsac)((6.5kg/m3)(20.49m/s2)-(0.4428kg/m3)(20.49m/s2)))-(0.1kg)(20.49m/s2)>0

(Vsac)(124.1kg/m2s2)>2.049kgm/s2

(Vsac)>0.0165m3

So the air sac, once fully inflated, has to be at least 0.0165m3: this is just slightly larger than a birthday balloon! 

Netflix Episode:

https://www.netflix.com/watch/80221410?trackId=13752289&tctx=0%2C1%2C0cf96766d87c94b430b3bda731c41e20cc39021f%3Ae8fbd308999a58f44d6604df1aec67f3b4e6732b%2C0cf96766d87c94b430b3bda731c41e20cc39021f%3Ae8fbd308999a58f44d6604df1aec67f3b4e6732b%2Cunknown%2C

Densities:

https://physics.info/density/